Analysis of the iteratively regularized Gauss-Newton method under a heuristic rule

作者：Jin, Qinian; Wang, Wei^*

来源：Inverse Problems, 2018, 34(3): 035001.

DOI：10.1088/1361-6420/aaa0fb

• nonlinear inverse problems
• the iteratively regularized Gauss-Newton method
• heuristic selection rule
• a posteriori error estimates
• convergence

The iteratively regularized Gauss-Newton method is one of the most prominent regularization methods for solving nonlinear ill-posed inverse problems when the data is corrupted by noise. In order to produce a useful approximate solution, this iterative method should be terminated properly. The existing a priori and a posteriori stopping rules require accurate information on the noise level, which may not be available or reliable in practical applications. In this paper we propose a heuristic selection rule for this regularization method, which requires no information on the noise level. By imposing certain conditions on the noise, we derive a posteriori error estimates on the approximate solutions under various source conditions. Furthermore, we establish a convergence result without using any source condition. Numerical results are presented to illustrate the performance of our heuristic selection rule.

• 出版日期2018-3
• 单位嘉兴学院